Lyapunov exponents are well-known characteristic numbers that describe growth rates of
perturbations applied to a trajectory of a dynamical system in different state space directions …

Recent years have witnessed a growing interest in covariant Lyapunov vectors (CLVs)
which span local intrinsic directions in the phase space of chaotic systems. Here, we review …

We study Lyapunov vectors (LVs) corresponding to the largest Lyapunov exponents in
systems with spatiotemporal chaos. We focus on characteristic LVs and compare the results …

We explore numerically the high-dimensional spatiotemporal chaos of Rayleigh-Bénard
convection using covariant Lyapunov vectors. We integrate the three-dimensional and time …

Fluids cooled to the liquid–vapor critical point develop system-spanning fluctuations in
density that transform their visual appearance. Despite a rich phenomenology, however …

We investigate Kardar-Parisi-Zhang (KPZ) surface growth in the presence of power-law
temporally correlated noise. By means of extensive numerical simulations of models in the …

Hyperbolicity is an important concept in dynamical system theory; however, we know little
about the hyperbolicity of concrete physical systems including fluid motions governed by the …

Finite-time Lyapunov exponents of generic chaotic dynamical systems fluctuate in time.
These fluctuations are due to the different degree of stability across the accessible phase …

Two sets of vectors, covariant Lyapunov vectors (CLVs) and orthogonal Lyapunov vectors
(OLVs), are currently used to characterize the linear stability of chaotic systems. A …

We study numerically a family of surface growth models that are known to be in the
universality class of the Kardar-Parisi-Zhang equation when driven by uncorrelated noise …